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Downloads
Views
Date
Relevance
Modeling Scenario
312
views
171
downloads
0
comments
3-054-Relay-ModelingScenario
We use a differential equations of one dimensional projectile motion and an integration of velocity for total distance to model the relay between an outfielder and an infielder in throwing the ball to home plate.
distance
projectile motion
relay
time
baseball
outfield
home plate
minimization
Modeling Scenario
239
views
129
downloads
0
comments
3-091-SpringModeling-ModelingScenario
In this lab students will collect data on their spring mass systems and compare their empirical models to their theoretical ones—giving them an opportunity to actually test a model against data.
data
laboratory
LoggerPro
Vernier
mass-spring system
model validation
empirical model
theoretical model
Modeling Scenario
177
views
175
downloads
0
comments
4-036-AltitudeDependentGravity-ModelingScenario
When projectiles are way above Earth's surface gravity's changes become important when dealing with projectiles at high altitudes. We lay out an approach for such a case which is a second-order differential equation.
a
gravity
projectile
linearization
ltitufe
altitude
Modeling Scenario
188
views
111
downloads
0
comments
3-020-ChordPathTime-ModelingScenario
Using Newton's Second Law of motion we can determine the time it takes for a mass to slide along a chord of a vertical circle from high point to any point along the circle. Initially, the result is nonintuitive and challenging to understand.
Unit Circle
path
falling
gravity
chord
Netwon's Second Law of Motion
Potential Scenario
134
views
50
downloads
0
comments
2007-I-Liang_Chern-Mathematical Modeling and Differential Equations
In this course, I will mainly focus on, but not limited to, two important classes of mathematical models by ordinary differential equations: • population dynamics in biology • dynamics in classical mechanics.
population dynamics
ecology
dynamics
classical mechanics
chemical reaction
Article or Presentation
137
views
36
downloads
0
comments
1980-Peastrel-Lynch-Armenti-Terminal_velocity_of_a_shuttlecock_in_vertical_fall
This paper offers a set of data on a falling shuttlecock (the moving object in badminton) in air. How the authors collected the data is described fully and can be replicated easily by modern equipment.
parameter estimation
data collection
resistance
falling
terminal velocity
Newton's Second Law of Motion
shuttlecock
Modeling Scenario
454
views
1067
downloads
0
comments
5-040-TunedMassDamper-Part-I-Modeling Scenario
We offer an opportunity to build mathematical models to mitigate dangerous displacements in structures using structural improvements called Tuned Mass Dampers. We model the motion of the original structure as a spring-mass-dashpot system.
structure
spring-mass-dashpot
spring mass
earthquake
vibration
tuned mass tuner
restoring force
control
dampe
Modeling Scenario
582
views
603
downloads
0
comments
3-043-BallisticModeling-SpongeDart-ModelingScenario
The goal of this project is for students to develop, analyze, and compare three different models for the flight of a sponge dart moving under the influences of gravity and air resistance.
projectile motion
air resistance
ballistics
dimensional analysis
Newtonian mechanics
sponge dart
Nerf gun
Nerf dart
Buckingham's Theorem
Modeling Scenario
333
views
718
downloads
0
comments
1-047-Condensation-ModelingScenario
We simulate the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall. Animations are produced and data is offered for modeling with a differential...
simulation
sum of square errors
condensation
best fit
Modeling Scenario
299
views
185
downloads
1
comments
1-092-DashItAll-ModelingSenario
This project uses very basic physics, Newton's Second Law of Motion, to model the motion of a sprinter running down a track. We derive the classic Hill-Keller model for a sprinter exerting ``maximum'' effort as he/she accelerates down a track.
data
running
sprint
Hill-Keller
world record
Olympics
Modeling Scenario
281
views
124
downloads
0
comments
1-105-AnimalFall-ModelingScenario
This project uses Newton's Second Law of Motion to model a falling animal with a resistance term proportional to cross sectional area of the animal, presumed to be spherical in shape.
animal
Netwon's Second Law of Motion
falling body
terminal velocity
air resistance
Newton
air friction
fall
Modeling Scenario
212
views
327
downloads
0
comments
3-090-OneSpringMass-ModelingScenario
We lead students through building a mathematical model for a single mass (bob)-spring system that is hanging vertically. We also lead the students, using data that they collect together with their model to approximate the value of the spring...
undamped
sum of square errors
mass spring
Hooke's Law
oscilation
least-squares approximation
Modeling Scenario
238
views
120
downloads
0
comments
6-012-RiverCrossing-ModelingScenario
Students develop a model of a river crossing in a boat with thrust using Newton's Second Law of Motion from a Free Body Diagram they construct. The model is thence a system of one second order linear and a second order nonlinear differential...
dragon
Newton's Second Law of Motion
river crossin
river current
velocity profile
thrust
Free Body Diagram
Modeling Scenario
264
views
142
downloads
0
comments
9-012-PDEGuitarTuning-ModelingScenario
We lead students through a derivation of a partial differential equation which models the motion of a string held at both ends, a case of the one-dimensional wave equation, and then play it on Mathematica.
extension
sine waves
frequency
guitar
damping
Fourier
string
tuning
Modeling Scenario
1007
views
145
downloads
0
comments
3-051-ProjectileMotions-ModelingScenario
We consider several instances of projectile flight without resistance, one on level ground and one from edge of cliff to determine maximum distance and placement.
trajectory
launching radiant
projectile motion
projectile
no resistance
angle of launch
Modeling Scenario
119
views
36
downloads
0
comments
3-052-OptimalProjectileFiring-ModelingScenario
We offer the opportunity to model a projectile's trajectory in several cases, all without resistance.
projectile motion
projectile
launch angle
maximum range
Modeling Scenario
548
views
221
downloads
0
comments
1-008-HangTime-ModelingScenario
We present a modeling opportunity for students in which they model the vertical position of a basketball player taking a jump shot. The goal of the scenario is to get students to consider the meaning of the notion ``hang-tune.''
gravity
hang tim
Newton's Second Law of Motion
jump shot
Modeling Scenario
283
views
153
downloads
0
comments
1-013-SleuthingWithDifferentialEquations-ModelingScenario
We present several situations in which differential equation models serve to aid in sleuthing and general investigations.
projectile motion
acceleration
Newton's Law of Cooling
speeding
Modeling Scenario
350
views
371
downloads
0
comments
1-047a-CondensationOptimization-ModelingScenario
We seek to optimize a condensation process which is modeled by a simulation using the random motion of 200 particles in a 50 by 50 square in which a particle bounces off the two vertical and top walls and condenses on the bottom wall.
simulation
data
optimization
energy
condensation
best fit
cost
sum of scquare errors
Modeling Scenario
296
views
247
downloads
0
comments
1-120-CircularRollerCoaster-ModelingScenario
Students study the dynamics of a circular roller coaster and work out the equations of motion in the ideal case as well as considering the interesting complication of including kinetic friction. This problem is an excellent introduction for students
population dynamics
energy
Fluid Mechanics
m
friction
roller coaster
integration by8 parts
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